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【ハイブリッドによる開催】東工大数論・幾何学セミナー：山口樹氏

講演タイトル: 　Ultra-test ideals for rings with finitely generated anti-canonical algebras
アブストラクト: 　 A ring homomorphism is said to be pure if its all base changes are injective. A natural question to ask is what singularities descend under pure morphisms. Boutot showed that rational singularities descend under pure morphisms. Recently, Godfrey and Murayama showed the case of Du Bois singularities, and Zhuang showed the case of singularities of klt type and plt type. In this talk, we prove a behavior of multiplier ideals under pure morphisms for rings with finitely generated anti-canonical algebras. Key tools for the proof are Schoutens’ ultraproduct method and the theory of F-singularities, a class of singularities characterized in terms of Frobenius morphisms.

更新日：2024.07.02